This paper deals with axisymmetric static and dynamic deformations of laminated hollow cylinders composed of an arbitrary number of monoclinic layers. The analysis is based on a successive approximation approach employed earlier by the authors for corresponding studies dealing with homogeneous orthotropic and cross-ply laminated cylinders. In the axisymmetric static case, where alternative approaches exist in the literature, the efficiency of the proposed approach is tested by means of comparisons of corresponding numerical results. However, the main purpose of the paper is an exact, three-dimensional, free vibration analysis of such angle-ply laminated cylinders. For this problem that has not as yet been considered in the literature, numerical results are presented and discussed for relatively thick cylinders having a regular symmetric or a regular antisymmetric angle-ply lay-up.